Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C17 · Schur multiplier (H2) = C27 |
| direct product | C17×#36679 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C17 | C24 |
| commutator, Frattini, cosocle | C23 | C25×C17 |
| socle | C23×C17 | C25 |
| prime radical | C22×D4×C17 | C23 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C17 ◁ G | |
1506 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 2176 |
A minimal faithful permutation representation — 5 generators on 49 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19)(20,23)(21,22)(24,25)(26,27)(28,30)(29,31)(32,33)(34,35,38,41)(36,42,44,39)(37,40,45,47)(43,48,49,46);(28,32)(30,33)(34,36,38,44)(35,39,41,42)(37,43,45,49)(40,46,47,48);(19,22)(23,25)(26,28)(27,30)(29,32)(31,33)(34,37,38,45)(35,40,41,47)(36,43,44,49)(39,46,42,48);(27,31)(28,32)(37,45)(40,47)(43,49)(46,48);(18,20,21,24)(19,23,22,25)884 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 29667);